On the Design of Codes for DNA Computing

  • Olgica Milenkovic
  • Navin Kashyap
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3969)


In this paper, we describe a broad class of problems arising in the context of designing codes for DNA computing. We primarily focus on design considerations pertaining to the phenomena of secondary structure formation in single-stranded DNA molecules and non-selective cross-hybridization. Secondary structure formation refers to the tendency of single-stranded DNA sequences to fold back upon themselves, thus becoming inactive in the computation process, while non-selective cross-hybridization refers to unwanted pairing between DNA sequences involved in the computation process. We use the Nussinov-Jacobson algorithm for secondary structure prediction to identify some design criteria that reduce the possibility of secondary structure formation in a codeword. These design criteria can be formulated in terms of constraints on the number of complementary pair matches between a DNA codeword and some of its shifts. We provide a sampling of simple techniques for enumerating and constructing sets of DNA sequences with properties that inhibit non-selective hybridization and secondary structure formation. Novel constructions of such codes include using cyclic reversible extended Goppa codes, generalized Hadamard matrices, and a binary mapping approach. Cyclic code constructions are particularly useful in light of the fact we prove that the presence of a cyclic structure reduces the complexity of testing DNA codes for secondary structure formation.


Secondary Structure Cyclic Code Hairpin Loop Cyclic Shift Goppa Code 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Olgica Milenkovic
    • 1
  • Navin Kashyap
    • 2
  1. 1.University of ColoradoBoulderUSA
  2. 2.Queen’s UniversityKingstonCanada

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